You can't carry in a National Park, but you can possess an unloaded weapon in your vehicle and you can have a loaded weapon in your tent, cabin, etc:
CFR, Title 36 - PARKS, FORESTS, AND PUBLIC PROPERTY
CHAPTER I - NATIONAL PARK SERVICE, DEPARTMENT OF THE INTERIOR
PART 2 - RESOURCE PROTECTION, PUBLIC USE AND RECREATION
Section 2.4 Weapons, traps and nets.
(a)(1) [...]
(2) Weapons, traps or nets may be carried, possessed or used:
(i) At designated times and locations in park areas where:
(A) The taking of wildlife is authorized by law in accordance with
Sec. 2.2 of this chapter;
(B) The taking of fish is authorized by law in accordance
with Sec. 2.3 of this part.
(ii) When used for target practice at designated times and at
facilities or locations designed and constructed specifically
for this purpose and designated pursuant to special regulations.
(iii) Within a residential dwelling. For purposes of this
subparagraph only, the term ``residential dwelling'' means a
fixed housing structure which is either the principal residence of
its occupants, or is occupied on a regular and recurring basis by
its occupants as an alternate residence or vacation home.
(3) Traps, nets and unloaded weapons may be possessed within a
Temporary lodging or mechanical mode of conveyance when such
implements are rendered temporarily inoperable or are packed,
cased or stored in a manner that will prevent their ready use.
(b) Carrying or possessing a loaded weapon in a motor vehicle,
vessel or other mode of transportation is prohibited, except that
carrying or possessing a loaded weapon in a vessel is allowed when
such vessel is not being propelled by machinery and is used as a
shooting platform in accordance with Federal and State law.